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Size:  481.3 KB hi I don't get why the limits for this set of questions are not changed because this is finding the area under the curve in respect to dt. So why aren't the values of t worked out like it did in this example ?Attachment 616220616222Attachment 616220616222616200 thanks
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    (Original post by coconut64)
    hi I don't get why the limits for this set of questions are not changed because this is finding the area under the curve in respect to dt. So why aren't the values of t worked out like it did in this example ?thanks
    Good question.

    If you're asked to find an integral \int^a_b \ (...) \ dt then this means the limits are with respect to t i.e. it means \int^{t=a}_{t=b}\ (...) \ dt.

    Similarly if you start with \int^a_b \ (...) \ dx then this means \int^{x=a}_{x=b} \ (...) \ dx so if you change to dt then you'll need to change the limits.
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    (Original post by coconut64)
    Name:  14859919190721209630434.jpg
Views: 23
Size:  481.3 KB hi I don't get why the limits for this set of questions are not changed because this is finding the area under the curve in respect to dt. So why aren't the values of t worked out like it did in this example ?Attachment 616220616222Attachment 616220616222616200 thanks
    limits change when you make a substitution and change what you are integrating with respect to. In the questions you are doing you are already integrating with respect to t so you dont need to make a sub and therefore you dont need to change limits
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    (Original post by coconut64)
    Name:  14859919190721209630434.jpg
Views: 23
Size:  481.3 KB hi I don't get why the limits for this set of questions are not changed because this is finding the area under the curve in respect to dt. So why aren't the values of t worked out like it did in this example ?Attachment 616220616222Attachment 616220616222616200 thanks
    In this question you are integrating with respect to t and so the limits are already defined in the question as being values of t. In the question where you are asked to find the area under the curve between to values of x, you integrate again with respect to t, but you need to figure out what values of t your x limits correspond to.
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    Very helpful, thank you all.
 
 
 
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